Solve the equation:

1. |x-7|=8
2. |x-9|=-14

Answer:

1 cent

Step-by-step explanation:

Dime = 10 cents

8 Dimes = 8 * 10 = 80 Cents

1 Nickel = 5 Cents

80 + 5 = 85

85 - 84 = 1 Cent

[tex]2800(0.95)^t~~ = ~~2800(b)^{\frac{t}{10}}\implies \cfrac{2800(0.95)^t}{2800}=b^{\frac{t}{10}}\implies 0.95^t=b^{\frac{t}{10}} \\\\\\ (0.95)^{\frac{10t}{10}}=b^{\frac{t}{10}}\implies (0.95^{10})^{\frac{t}{10}}=b^{\frac{t}{10}}\implies (0.5987)^{\frac{t}{10}}\approx b^{\frac{t}{10}}\implies 0.5987 \approx b \\\\[-0.35em] ~\dotfill\\\\ ~\hfill f(t)\approx 2800(0.5987)^{\frac{t}{10}}~\hfill[/tex]

Work Shown:

i = P*r*t

i = 3000*0.025*4

i = 300

Answer:

Step-by-step explanation:

To get one portion of soup, each ingredient should be divided by 3

Quantity of onion required=  180 ÷ 3 = 60 g

Quantity of carrots required = 120 ÷ 3 = 60 g

Oil = 3 ÷ 3 = 1 table spoon

Quantity of tomatoes required = 600 ÷ 3 = 300 g

Vegetable stock = 1.2 ÷ 3 = 0.4 litres

Answer:

  $10,596.81

Step-by-step explanation:

The balance on an account earning 5% interest compounded quarterly can be found using the formula ...

  A = P(1 +0.05/4)^(4t)

where P is the principal invested and t is the number of years.

__

Here, we are investing $7500.00. After 2 years, the account balance will be ...

  A = $7500(1 +0.05/4)^(4·2) = $8283.65

After the $1500 withdrawal, the new balance will be ...

  $8583.65 -1500.00 = $6783.65

__

This is the amount earning interest for the next year, after which time the balance will be ...

  A = $6783.65·(1.0125)^(4·1) = $7129.24

When $2000 is added to the account, the principal earning interest for the last 3 years is ...

  $7129.24 +2000.00 = $9129.24

__

The final balance after 3 more years is then ...

  A = $9129.24·(1.0125)^(4·3) = $10,596.81

_____

These calculations are conveniently carried out by a spreadsheet, as in the attached. Since the account changes are all done at the end of the year, we don't have to keep track of the quarterly balances. The formula used to calculate the ending balance each year is shown.

Answer:

Step-by-step explanation:

Equation

Part A

# Calculators = Total amount / Cost of 1 calculator

Givens

# Calculators = ?

Total amount of money = 195 dollars

Cost of one calculator = 6.50

Solution

# Calculators = 195/6.50

# Calculators = 30

Answer: He can buy 30 calculators.

The bucket that contains 2120 grams of sand and a cup that contains 438 grams of sand , the bucket of sand has 1682 grams of sand than the cup of sand in the cup.

A cup contains 438 grams of sand. A bucket contains 2120 grams of sand.

Therefore, the number of more grams of sand in the bucket than the cup is as follows:

mass of sand in cups = 438 grams

mass of sand in the bucket = 2120 grams

Therefore,

difference in mass = 2120 - 438

difference in mass = 1682 grams

Therefore, they are 1682 grams of sands in the bucket than the cup.

learn more on mass(grams) here: https://brainly.com/question/12843854

Answer:

See below ↓

Step-by-step explanation:

3.

4.

5.

Answer:

P=300cm

Step-by-step explanation:

P=4a=4.75×4=300cm

[tex]\green{ \underline { \boxed{ \sf{Perimeter \: of \:Square = 4 \times side }}}}[/tex]

Putting Values -

[tex]\begin{gathered}\\\implies\quad \sf Perimeter \:of \:Square = 4 \times 75 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf Perimeter \: of \:Square = 300 sq. \:cm \\\end{gathered} [/tex]

>>Therefore, Perimeter of the Square is 300 sq. cm

Answer:

-> See attached

115.893 meters²

Step-by-step explanation:

   See attached for my sketch.

    Area for a rectangle is A = L * W:

9.78 meters * 11.85 meters = 115.893 meters²

Answer:

1/8

Step-by-step explanation:

1/4 ÷ 2 = 0.125

0.125 as a decimal is 1/8

Answer:

Step-by-step explanation:

firstly the area for teh rectangle is 12 x 15 = 18are0

the area for the circle is 113.1 sq inches because  pi x r squared

Answer:

see explanation

Step-by-step explanation:

look at the photo

Answer:

B is the right answer

Step-by-step explanation:

Subtract 14 from each side to get the value of m

21 - 14 = 7 = m

m = 7

Answer:10/7 and mixed number form is 1 3/7

Tim covered 21.333 kilometers

Kilometers, km covered is distance, d

d = speed / time

d = 80 / 3 hours 45 mins

Converting 45 mins to hours we have

1 hour = 60 minutes

? Hours = 45 minutes

? = 45 / 60 = 0.75

So time is 3.75 hours

d = 80 / 3.75

= 64 / 3

= 21.333km

hope it helps

Answer:

300 km

Step-by-step explanation:

Tim drives 80 km in 1 hour or 60 minutes

Tim drives in 1 minute = 80/60 km

so, tim drives in 3 hours 45 minutes ( 225 minutes)

[tex] \frac{80 \times 225}{60} [/tex]

= 300 km

Answer:

Step-by-step explanation:

12g - 17 ≥ 17

12g ≥ 34

g ≥ [tex]\frac{34}{12}[/tex]

g ≥ [tex]\frac{17}{6}[/tex]

Step-by-step explanation:

Given point are: P(at², 2at)

Q(a/t², 2a/t)

S(0, 0)

Now, the distance between A(x₁y₁) and B(X₂, y₂)

then AB = √{(x₂ - x₁)² + (y₂ - y₁)²} units

(i) The distance between S and P:

(x₁, y₁) = (0, 0) ⇛x₁= 0, y₁ = 0

(x₂, y₂ ) = (at², 2at) ⇛x₂ = at², y₂ = 2at

SP = √{at² - 0)² + (2at - 0)²}

= √{(at²)² + (2at)²}

= √{a²t²*² + 4a²t²}

= √{a²t⁴ + 4a²t²}

= √{a²t²(t²+4)}

SP = at√(t² + 4)→→→Eqn(1)

(ii) The distance between S and Q :

(x₁, y₁) = (0, 0) ⇛x₁= 0, y₁ = 0

(x₂, y₂ ) = (a/t², 2a/t) ⇛x₂ = a/t², y₂ = 2a/t

SQ = √[{(a/t²) - 0} + {(2a/t) - 0}

= √{(a/t²)² + (2a/t)²}

= √{(a²/t²*²) + (4a²/t²)}

= √{(a²/t⁴) + (4a²/t²)}

= √{(a² + 4a²t²)/t⁴}

= √[{a²(1 + 4t²)}/t⁴]

SQ = (a/t²)√(1 + 4t²) →→→ Eqn(2)

Now,

(1/SP) + (1/SQ) = [1/{at√(t² + 4)}] + [1/{(a/t²)√(1 + 4t²)}]

= (1/at)[1/{√(t² + 4)}] + (t²/a)[1/{(√1 + 4t²)}]

= (1/a)[[1/{t√(t² + 4)}] + [t²/{√(1 + 4t²)}]]

(1/SP) + (1/SQ) = 1/a is not independent of 't'

If suppose S = (a, 0) then

SP = √{(at² - a)² + (2at - 0)²}

= √{a²(t² - 1)² + (2at)²}

= a√{(t² - 1)² + 4t²}

= a√{(t² + 1)²}

SP = a(t² + 1)

1/SP = 1/{a(t² + 1)} →→→Eqn(1)

And

SQ = √[{(a/t²) - a}² + {(2a/t) - 0}²]

= √[a²{(1/t²) - 1}² + a²(2/t)²]

= a√[{(1 - t²)²/t⁴} + (4/t²)]

= a√[{(1 - t²)² + 4t²}/t⁴]

( a/t²)√(1 + t²)²

SQ = (a/t²)(1 + t²)

1/SQ = 1/{(a/t²)(1 + t²)} = t²/{a(1 + t²)} →→→Eqn(2)

Therefore, (1/SP) + (1/SQ)

= 1/{a(t² + 1)} + t²/{a(1 + t²)}

= (1 + t²)/a(1 + t²)

= 1/a

1/a is independent of 't'.

[tex]2x {}^{2} - x - 4[/tex]

[tex]x = \frac{ - ( - 1) + \sqrt{1 - 4(2)( - 4)} }{2(2)} = \frac{1 + \sqrt{33} }{4} [/tex]

[tex]x = \frac{1 - \sqrt{33} }{4} [/tex]

[tex](x - \frac{1 + \sqrt{33} }{4} )(x - \frac{1 - \sqrt{33} }{4} )[/tex]

[tex](4x - 1 - \sqrt{33} )(4x - 1 + \sqrt{33} )[/tex]

Answer:

A

Step-by-step explanation:

Find the number of bottles in 5 cases:

5 × 12 = 60

Find the number of liters in 60 bottles:

60 × 3 = 180

180 liters of laundry detergent

The function N =1053(1.23)^m or 1053(1.23)^m = N is an illustration of an exponential function

The function is given as:

N =1053(1.23)^m

On April 1, 2016; the value of m is:

m = 0

So, we have:

N =1053(1.23)^0

N = 1053

Hence, there are 1053 deers on April 1, 2016

The function is given as:

N =1053(1.23)^m

On April 1, 2016; the value of m is:

m = 1

So, we have:

N =1053(1.23)^1

N =1295

Hence, there are 1295 deers on May 1, 2016

An exponential growth function is represented as:

y = a(1 + r)^x

Where r represents the growth rate

By comparison; the monthly growth rate (r) is calculated as:

1 + r = 1.23

Subtract 1 from both sides

r = 0.23

Express as percentage

r = 23%

Hence, the monthly growth rate is 23%

We have the monthly growth rate to be 23%

There are 12 months in a year.

So, the yearly growth rate is:

y = 23%^12

Evaluate

y = 0.00022%

Hence, the yearly growth rate is 0.00022%

We have the monthly growth rate to be 23%

There are 4 weeks in a months

So, the weekly growth rate is:

m = 23%^(1/4)

Evaluate

m = 69%

Hence, the weekly growth rate is 69%

Read more about exponential functions at:

https://brainly.com/question/11464095

Answer: 13

Step-by-step explanation:

Answer:

Hey Dude....

Step-by-step explanation:

This is ur answer.....

Hope it helps!

Brainliest pls!

Follow me! :)

Answer:

Acute angle

Step-by-step explanation:

Acute angle = less than 90 degrees

Answer:

acute angles

Step-by-step explanation:

Angles between 0 and 90 degrees (0°< θ <90°) are called acute angles. Angles between 90 and 180 degrees (90°< θ <180°) are known as obtuse angles. Angles that are 90 degrees (θ = 90°) are right angles.

Answer:

  50.32 cm²

Step-by-step explanation:

The area of a triangle can be computed using the formula ...

  A = 1/2bh

For a triangle with base 3.7 cm and height 6.8 cm, the area is ...

  A = 1/2(3.7 cm)(6.8 cm) = 12.58 cm²

__

For four (4) triangles, Señora Cruz will need 4 times this area:

  4 × (12.58 cm²) = 50.32 cm²

Señora Cruz will need 50.32 cm² of paper to create her door decor.

[tex]\sf y=50\left(1.8\right)^{x}[/tex]

=================================

the first term : 50

crosses point : (0, 50), (1, 90)

solve for y,

[tex]\sf y=50\left(1.8\right)^{1}[/tex]

[tex]\sf y=90[/tex]

Graph:

All cases rewritten in the form of difference expressions are listed below:

Equalities represent relationships between two expressions, in which one expression is equal to another. An equality (x = a) is equivalent to the following difference expression:  

x - a = 0   (1)

And inequalities represent relationships between two expressions, in which one expression is not necessarily to another. An inequality (x < a, x > a, x ≤ a, x ≥ a) is represented by the following difference expression:

x - a = b   (2)

Where b have the following cases:

Now we proceed to rewrite each case in term of difference expressions:

To learn more on inequalities, we kindly invite to check this verified question: https://brainly.com/question/19491153

Answer:

301 feet

Step-by-step explanation:

plug in the known values

[tex]85=\sqrt{24d}[/tex]

square both sides to cancel the square root

[tex]7225=24d[/tex]

divide both sides by 24 to get d on its own

[tex]d=301.041[/tex] feet

to the nearest foot is 301 feet

Answer:

A. 3.5

Step-by-step explanation:

The perimeter is just the sum of all of the side lengths. The sides of this triangle are n inches, (n + 5.2) inches, and (2n + 3.4) inches.

So, your equation is n + n + 5.2 + 2n + 3.4 = 22.6 inches.

You can combine like terms (adding together all of the n's and all of the numbers) to simplify your equation to 4n + 8.6 = 22.6 inches.

Subtract 8.6 from both sides of the equation to get 4n = 14, and divide both sides by 4 to get n = 3.5.

Hope this helps! :)

Answer:

0.00236

Step-by-step explanation:

Move the decimal left 3 times as the exponent is negitiave 3